Why doesn’t any rabbi do parah adumah?
The main difficulty concerning performing the ritual of parah adumah today is that there are no cohanim that we can certify as being ritually pure. As the Mishnah teaches, the only way to ensure this is by bringing up a child in relative seclusion (he may live with his family, but in an area that is ‘safe’ from ritual defilement), ensuring that he does not become temei mes (other forms of tumah are not problematic, because immersion in a mikvah would solve the problem). In addtion, we can’t wait for a cow, and then begin to bring up a cohen child in ritual purity, because by the time he reached the age of thirteen the cow would most likely be dead, or at least disqualified.
There are some who wish to perform the ritual of parah adumah, and have suggested bringing up children in semi-seclusion for this purpose. As of yet, this has not been done.
Sources: See Mishnah, Parah 3:2.